created, =this.created & modified, =this.modified
tags:sciencemathcs
Excursions to the edge of thought
Tragic Arc:
rel:When We Cease To Understand the World by Labatut
More often the life has a tragic arc. The originator of group theory, Évariste Galois, was killed in a duel before he reached his twenty-first birthday. The most revolutionary mathematician of the last half century, Alexander Grothendieck, ended his turbulent days as a delusional hermit in the Pyrenees. The creator of the theory of infinity, Georg Cantor, was a kabbalistic mystic who died in an insane asylum. Ada Lovelace, the cult goddess of cyber feminism (and namesake of the programming language used by the U.S. Department of Defense), was plagued by nervous crises brought on by her obsession with atoning for the incestuous excesses of her father, Lord Byron. The great Russian masters of infinity, Dmitri Egorov and Pavel Florensky, were denounced for their antimaterialist spiritualism and murdered in Stalin’s Gulag. Kurt Gödel, the greatest of all modern logicians, starved himself to death out of the paranoiac belief that there was a universal conspiracy to poison him. David Foster Wallace (whose attempt to grapple with the subject of infinity I examine) hanged himself. And Alan Turing—who conceived of the computer, solved the greatest logic problem of his time, and saved countless lives by cracking the Nazi “Enigma” code—took his own life, for reasons that remain mysterious, by biting into a cyanide-laced apple.
How does thought interact with the tangible world:
Then there’s epistemology. Most great mathematicians claim insight into an eternal realm of abstract forms transcending the ordinary world we live in. How do they interact with this supposed “Platonic” world to obtain mathematical knowledge? Or could it be that they are radically mistaken—that mathematics, for all its power and utility, ultimately amounts to a mere tautology, like the proposition “A brown cow is a cow”?
Beauty and truth:
rel:Understanding the opossum
Physicists, too, are prone to a romantic image of how they arrive at knowledge. When they don’t have hard experimental/observational evidence to go on, they rely on their aesthetic intuition—on what the Nobel laureate Steven Weinberg unblushingly calls their “sense of beauty.” The “beauty = truth” equation has served physicists well for much of the last century. But… has it recently been leading them astray?
When Einstein Walked with Gödel
Einstein on Princeton, Princeton is a wonderful piece of earth, and at the same time an exceedingly amusing ceremonial backwater of tiny spindle-shanked demigods
Einstein and Gödel had contrasting demeanors but Einstein told people that he went to his office “just to have the privilege of walking home with Kurt Gödel.” United by a shared sense of intellectual isolation, they found solace in their companionship.
Gödel was especially preoccupied by the nature of time, which, he told a friend, was the philosophical question. How could such a “mysterious and seemingly self-contradictory” thing, he wondered, “form the basis of the world’s and our own existence”?
Gödel intended to study physics but was seduced by math and the notions that abstractions like numbers and circles had perfect, timeless existence independent of the human mind (Platonism). In Vienna Circle these ideas were considered old fashioned.
What made a proposition like “2 + 2 = 4” true, they held, was not that it correctly described some abstract world of numbers but that it could be derived in a logical system according to certain rules.
Gödel’s self- referential formula comments on its provability, not on its truthfulness.
1st theorem: no logical system can capture all the truths of math. 2nd theorem: no logical system for math could, by its own devices, be shown to be free for inconsistency.
Rather than believing he had shattered the ideal of complete knowledge, Gödel believed he had shown that mathematics has a robust reality that transcends any system of logic. He believed we had “mathematical intuition” and logic was not the only route to knowledge of reality.
It is this faculty of intuition that allows us to see, for example, that the formula saying “I am not provable” must be true, even though it defies proof within the system where it lives.
Der Nachtfalter (the Moth) he met Adele his wife.
Gödel took the matter of citizenship with great solemnity, preparing for the exam by making a close study of the U.S. Constitution. On the appointed day, Einstein accompanied him to the courthouse in Trenton and had to intervene to quiet Gödel down when the agitated logician began explaining to the judge how the U.S. Constitution contained a loophole that would allow a dictatorship to come into existence.
Gödel explored time: If time travel is possible, he submitted, then time itself is impossible. A past that can be revisited has not really passed. And the fact that the actual universe is expanding, rather than rotating, is irrelevant. Time, like God, is either necessary or nothing; if it disappears in one possible universe, it is undermined in every possible universe, including our own.
Einstein to Queen Elisabeth of Belgium, “the exaggerated esteem in which my lifework is held makes me very ill at ease. I feel compelled to think of myself as an involuntary swindler.” He died a month later, at the age of seventy-six. When Gödel and another colleague went to Einstein’s office at the institute to deal with his papers, they found the blackboard covered with dead-end equations.
A certain futility marked the last years of both Gödel and Einstein.
William Blake, “I see the Past, Present and Future existing all at once / Before me”.
Time — the Grand Illusion?
We are stubbornly in thrall to our temporal illusions. We cannot help feeling ourselves to be slaves to one part of the timescape (the past) and hostages to another part (the future)
Specious present
The time duration wherein one’s perceptions are considered to be in the present. Text says this interval is three seconds.
rel:Time Perception
Most physicists and philosophers today agree with Einstein that time’s passage is an illusion; they are eternalists. But a minority—who call themselves presentists—think that now is a special moment that really advances, like a little light moving along the line of history; this would still be true, they believe, even if there were no observers like us in the universe.
The Neuroscience of Math
Acalculia, a general term for number processing defects. The subject of a brain lesion, Mr. N was incapable of certain calculation. 2+2 = 3. He could count a recite a sequence, but not count down from nine, or recognize odd or even numbers.
There were fragmentary abilities maintained. He could know the correct quantity, but reciting the sequence was his only way of retrieving the corresponding word.
Dehaene’s work raises crucial issues about the way mathematics is taught. In his view, we are all born with an evolutionarily ancient mathematical instinct. To become numerate, children must capitalize on this instinct, but they must also unlearn certain tendencies that were helpful to our primate ancestors but that clash with skills needed today.
Number sense: in experiments subjects answered comparisons of number magnitude faster when the numbers were further apart. (2 and 9, versus 5 and 6.) As magnitude increased they were also more difficult (2 and 3, versus 8 and 9.)
But the brain is the product of evolution—a messy, random process— and though the number sense may be lodged in a particular bit of the cerebral cortex, its circuitry seems to be intermingled with the wiring for other mental functions.
rel:Orientational Metaphors
Dehaene noticed that subjects performed better with large numbers if they held the response key in their right hand but did better with small numbers if they held the response key in their left hand. Strangely, if the subjects were made to cross their hands, the effect was reversed. The actual hand used to make the response was, it seemed, irrelevant; it was space itself that the subjects unconsciously associated with larger or smaller numbers
Using technology/calculator: Our built-in ineptness when it comes to more complex mathematical processes has led Dehaene to question why we insist on drilling procedures like long division into our children at all.
A learning tool with balancing: (developed) The Number Race to help dyscalculic children. The software is adaptive, detecting the number tasks where the child is shaky and adjusting the level of difficulty to maintain an encouraging success rate of 75 percent.
Much of what our mind does with numbers is subconscious leading to “wonder why some mental activity crosses the threshold of awareness and some doesn’t. “
Riemann Zeta Conjecture and the Laughter of the Primes
Implications of the Copernican Principle for Our Future Prospects in 1993 by J. Richard Gott III.
Humans have been around for 200K years. Paper says 95% chance 5.1K years further, but disappearing within 7.8 million.
Says, Laughter and numbers will exist, but not the internet nor baseball. Both exist in Chimps.
More “math beauty”:
“Rightly viewed,” Russell wrote, mathematics “possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.”
There are infinitely many primes, so we consider how scattered they are. Twin primes (those who are differing by only by two, an open question to if there are infinitely many) crop up at random.
Riemann zeta hypothesis is more than just the key to understanding primes, but it is so central to math progress that its truth has been assumed, in provisional proofs of thousands of theorems.
The zeta function, fittingly, has its origins in music. If you pluck a violin string, it vibrates to create not only the note to which it is tuned but also all possible overtones. Mathematically, this combination of sounds corresponds to the infinite sum 1 + ½ + ⅓ + ¼ +…, which is known as the harmonic series. If you take every term in this series and raise it to the variable power s, you get the zeta function.
Each zero of the zeta function, when fed into Riemann’s prime formula, produces a wave resembling a pure musical tone. When these pure tones are all combined, they generate the harmonic structure of the prime numbers.
Sir Francis Galton, Father of Statistics… and Eugenics
1880s, Francis Galton (“whatever you can, count” rel:Datasets - Shoes through the years) concealed in his pocket a “pricker” which was a needle mounted on a thimble and a cross-shaped piece of paper, which he prickled holes into to rate the looks of female passersbys to create a “beauty map” of the British Isles.
Galton was the father of eugenics, and Darwin’s Origin of the Species filled him with a sense of clarity and purpose.
Leaping beyond Darwin, who had thought mainly about the evolution of physical features, like wings and eyes, Galton applied the same hereditary logic to mental traits, like talent and virtue.
Galton coined “nature versus nurture” (suggested in Shakespeare’s Tempest “A devil, a born devil, on whose nature / Nurture can never stick”)
To mistake regression for a real force that causes talent or quality to dissipate over time, as so many have, is to commit what has been called Galton’s fallacy.
Some of Galton’s interests
- submarine glasses which allowed reading while submerged
- arithmetic by smell paper
- strawberry cure for gout paper
- statistical efficacy of prayer
- a celestial signaling system for the martians
What nature does blindly, slowly, and ruthlessly, man may do providently, quickly, and kindly,” he declared.
A Mathematical Romance
For those who have learned something of higher mathematics, nothing could be more natural than to use the word “beautiful” in connection with it
G. H. Hardy, declared that beauty, not usefulness, is the true justification for mathematics.
“Beauty is the first test: there is no permanent place in the world for ugly mathematics.”
The Langlands program - aims at being a grand unifying theory, containing “the source code for all mathematics”
What Galois saw was a truly beautiful way to extend the symmetry concept into the realm of numbers.
(Interrogator: “What is the definition of a circle?” Frenkel: “A circle is the set of points on the plane equidistant from a given point.” Interrogator: “Wrong! It’s the set of all points on the plane equidistant from a given point.”)
As with Galois theory, the Langlands program had its origins in a letter.letters
The Langlands program is a scheme of conjectures that would turn such hypothetical analogies into sturdy logical bridges, linking up diverse mathematical Islands across the surrounding sea of ignorance.
Frenel’s take is different, that mathematical structures are the objects of reality, also as real as the physical or mental:
“How can it be,” Einstein asked in wonderment, “that mathematics, being after all a product of human thought independent of experience, is so admirably appropriate to the objects of reality?”
Oh god…
Inspired by Yukio Mishima’s Rite of Love and Death, he titled it Rites of Love and Math. In this silent Noh- style allegory, Frenkel plays a mathematician who creates a formula of love. To keep the formula from falling into evil hands, he hides it away from the world by tattooing it with a bamboo stick on the body of the woman he loves and then prepares to sacrifice himself for its protection.
The only numbers in it are 0, 1, and ∞. Isn’t love like that?
The Avatars of Higher Mathematics
Hardy argued that the point of mathematics was the same as the point of art: the creation of intrinsic beauty… No doubt Hardy, who died in 1947, would be distressed to learn that his “pure” number theory has been pressed into impure service as the basis for public-key cryptography
Even at France’s elite École Polytechnique, 70 percent of the mathematics students today aspire to a career in finance.
rel:The Routledge Handbook of Semantics
Grothendieck’s vision of mathematics led him to develop a new language—it might even be called an ideology—in which hitherto unimaginable ideas could be expressed. He was the first to champion the principle that knowing a mathematical object means knowing its relations to all other objects of the same kind. In other words, if you want to know the real nature of a mathematical object, don’t look inside it but see how it plays with its peers.
The play in one category—say, the category of surfaces—might be subtly mimicked by the play in another— say, the category of algebras. The two categories themselves can be seen to play together: there is a natural way of going back and forth between them, called a functor. rel:Transmutation and Transformation
Emmy Noether and Grothendieck who said that he liked to solve a
problem not by the “hammer-and-chisel method” but by letting a sea of
abstraction rise to “submerge and dissolve” it.” rel:Islands
The old things turned out to be mere shadows—or, as Grothendieck preferred to call them, “avatars”—of the new. (An avatar is originally an earthly manifestation of a Hindu god; perhaps because of the influence of André Weil, who was also an expert in Sanskrit, many French mathematicians have a terminological predilection for Hindu metaphysics.) Strange and intelligent - Why Simone Weil is the patron saint of anomalous persons
Harris: If you were to ask for a single characteristic of contemporary mathematics that cries out for philosophical analysis, I would advise you to practice climbing the categorical and avatar ladders in search of meaning, rather than searching for solid Foundations.
Benoit Mandelbrot and the Discovery of Fractals
Segment of self-similarity: The closer you look at a coastline, the more you find it is jagged, not smooth, and each jagged segment contains smaller, similarly jagged segments.
Fractal, fractus = broken in latin.
He also credits the “outdated” math books he happened to get his hands on as a teenage émigré, which had more pictures than those used in school then (and today).
Mandelbrot was motivated by Zipf’s law.
Title
stating that when a list of measured values is sorted in decreasing order, the value of the n-th entry is often approximately inversely proportional to n.
For example, in the Brown Corpus of American English text, the word “the” is the most frequently occurring word, and by itself accounts for nearly 7% of all word occurrences (69,971 out of slightly over 1 million). True to Zipf’s law, the second-place word “of” accounts for slightly over 3.5% of words (36,411 occurrences), followed by “and” (28,852).
The principle of least effort is another possible explanation: Zipf himself proposed that neither speakers nor hearers using a given language wants to work any harder than necessary to reach understanding, and the process that results in approximately equal distribution of effort leads to the observed Zipf distribution.
Pure research at IBM: Best of all, he could use IBM’s computers to make geometric pictures. Programming back then was a laborious business that involved transporting punch cards from one facility to another in the backs of station wagons.
Passwords: When his son’s high school teacher sought help for a computer class, Mandelbrot obliged, only to find that soon students all over Westchester County were tapping into IBM’s computers by using his name. “At that point, the computing center staff had to assign passwords,” he says. “So I can boast—if that’s the right term—of having been at the origin of the police intrusion that this change represented.”
rel:Islands
The world we live in, Mandelbrot observes, is an “infinite sea of complexity.” Yet it contains two “islands of simplicity.” One of these, the Euclidean simplicity of smooth forms, was discovered by the ancients. The other, the fractal simplicity of self-similar roughness, was largely discovered by Mandelbrot himself.
Higher Dimensions and Abstract Maps
Geometrical Creatures
On Abbott’s Flatland: A Romance of Many Dimensions
The first philosophers to talk about a “fourth dimension” were the seventeenth-century Cambridge Platonists, but they seemed to have something more spiritual than spatial in mind.
Descartes added an extra variable in his coordinate geometry, which allowed him to define four-dimensional sursoildes. John Wallis denounced the sursoildes as “Monster in Nature, less possible than the Chimera or Centaur.”
In 1907, Hinton wrote a sort of sequel to Abbott’s book, which he titled An Episode of Flatland which focused on the fourth dimension. Hinton added to this the “method of shadows,” whereby one tries to grasp a 4-D object by considering the 3-D shadows, or projections, it casts from various angles. One projection of a hypercube, for example, looks like a small 3-D cube inside of a larger one—an object that Hinton dubbed a “tesseract.” Finally, there is the “method of unfolding.”shadows
Comedy of Colors
On four color map theorem Four Color Theorem
The human part of the argument, comprising some seven hundred pages, was daunting enough. But the in silico part, which yielded a four- foot-high computer printout, could never be humanly verified, even if all the mathematicians in the world set themselves to the task. It was as though a key stage in the reasoning had been supplied by an oracle in the form of a long sequence of “yeses.” If a single one of these “yeses” should have been a “no,” the entire proof would be worthless.
Infinite Visions: Georg Cantor v. David Foster Wallace
rel: Infinity - Ian Stewart
Aristotle was moved to ban the idea of a “completed” infinity from Greek thought, setting the orthodoxy for the next two thousand years.
Cantor used the collapse of the familiar logic of part and whole to define a new concept of infinity which didn’t rely on a vague notion of endlessness. An infinite set is one that is the same size as some of its parts. It can lose some of its members without being diminished.
Given any infinite set, you can always come up with a larger infinity by considering its “power set”—the set of all subsets that can be formed from it.
Others, however, dismissed Cantor’s infinity of infinities as a “fog on a fog” and “mathematical insanity.”
Worshipping Infinity
Many mathematicians, even quite prominent ones, openly avow their belief in a realm of perfect mathematical entities hovering over the grubby empirical world—a sort of Platonic heaven.
Roger Penrose: the natural world is but a shadow of the Platonic realm of eternal mathematical forms.
Cantor did not set out to characterize the infinite for its own sake; rather, he claimed, the idea “was logically forced upon me, almost against my will.”
Members of the sect believed that by repetitively chanting God’s name, they could achieve fusion with the divine. Name Worshipping, traceable to fourth-century Christian hermits in the deserts of Palestine, was revived in the modern era by a Russian monk called Ilarion. In 1907, Ilarion published On the Mountains of the Caucasus, a book that described the ecstatic experiences he induced in himself while chanting the names of Christ and God over and over again until his breathing and heartbeat were in tune with the words.
The Russians were convinced they could summon new mathematical entities into existence merely by naming them.
Grothendieck: Like the Russian Name Worshippers, the authors of Naming Infinity note, he saw naming “as a way to grasp objects even before they have been understood.” (framework enabling its practitioners to express hitherto inexpressible ideas)
The Dangerous Idea of the Infinitesimal
The infinitely great lies without, at the circumference of all things; the infinitesimal lies within, at the center of all things.
You could divide up space as finely as you pleased, Aristotle said, but you could never reduce it to an infinite number of parts.
In 1821, the great French mathematician Augustin Cauchy took the first step by exploiting the mathematical notion of a “limit.”
The most dramatic discovery that has been made by model theorists is that there is a fundamental indeterminacy in semantics—in the relationship between language and reality. A theory in a formal language, it turns out, is usually incapable of pinning down the unique reality it is supposed to describe. The theory will have “unintended interpretations” in which its meanings are twisted.
Our most vivid sense of the infinitely small, however, may spring from our own finitude in the face of eternity, the thought of which can be at once humbling and ennobling. This idea, and its connection to the infinitely small, was expressed in a poignant way by Scott Carey, the protagonist of the 1950s film The Incredible Shrinking Man, as he seemed to be dwindling into nonexistence at the end of the movie, owing to the effect of some weird radiation. “I was continuing to shrink, to become— what?—the infinitesimal,” he meditates,
So close, the infinitesimal and the infinite. But suddenly I knew they were really the two ends of the same concept. The unbelievably small and the unbelievably vast eventually meet, like the closing of a gigantic circle. I looked up, as if somehow I could grasp the heavens. And in that moment I knew the answer to the riddle of the infinite. I had thought in terms of man’s own limited dimensions. I had presumed upon nature. That existence begins and ends is man’s conception, not nature’s. And I felt my body dwindling, melting, becoming nothing. My fears melted away. And in their place came acceptance. All this vast majesty of creation—it had to mean something. And then I meant something too. Yes, smaller than the smallest, I meant something too. To God, there is no zero. I still exist.
Computer Age
Ada Lovelace
NOTE
A bit of a negative account of Ada.
Augusta Ada Byron, Lovelace, died in 1852 at the age 36 (the same age as her father.)
At thirteen, she underwent an episode of hysterical blindness and paralysis. At sixteen, despite the constant surveillance of a coven of her mother’s spinster friends (“the Furies,” Ada called them), she managed to steal away for a spot of lovemaking with her tutor.
Discussed elsewhere in ID but:
Finally, the architecture of the Analytical Engine was quite like that of a modern computer: it had a “store” (memory), a “mill” (processor), and an input device for entering programs and an output device for printing results.
Stressing that the Analytical Engine was to be programmable by punched cards, like the automatic French looms, she wrote that it “weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves.”
Ada depended on the “Opium system” for what tranquillity she could obtain. On one occasion, apparently under its influence, she had a vision of herself as the sun at the center of her own planetary system.
Ada excelled in the “poetic science.”
Text states perhaps the first programmer could be considered Jacquard.
Alan Turing
NOTE
Summary of Turing’s life and questions surrounding the nature of his death.
Halting State and Decision Problem:
For instance, there could be no Turing machine that, when fed with the program number of another machine, would decide whether that machine would eventually come to a halt in its computation or would grind on forever.
Turing was able to prove that no computing machine of the kind he envisaged could solve the decision problem. Reasoning could not be reduced to computation after all.
Church arrived at Lambda calculus.
Wittgenstein and Turing: Back at Cambridge, he became a regular at Ludwig Wittgenstein’s seminar on the foundations of mathematics. Turing and Wittgenstein were remarkably alike: solitary, ascetic, homosexual, drawn to fundamental questions. But they disagreed sharply on philosophical matters, like the relationship between logic and ordinary life. “No one has ever yet got into trouble from a contradiction in logic,” Wittgenstein insisted. To which Turing’s response was “The real harm will not come in unless there is an application, in which case a bridge may fall down.”
Turing:
I am more interested in the possibility of producing models of the action of the brain than in the practical applications of computing,” he wrote to a friend. Turing conjectured that, initially at least, computers might be suited to purely symbolic tasks, presupposing no contact with the outside world.
The news of Turing’s conviction received no national attention.
He also, a few months before his death, sent a friend a series of postcards containing eight “messages from the unseen world.”
- science is a differential Equation. Religion is a boundary condition.
- Hyperboloids of wondrous light / Rolling for aye through space and time / harbour those waves which somehow might / play out God’s wondrous pantomime”
- The Universe is the interior of the Light Cone of the Creation.
Dr. Strangelove Makes a Thinking Machine
MANIAC - Mathematical and Numerical Integrator and Computer. The first job was to do the calculation necessary to engineer the prototype of the hydrogen bomb.
Difficulties of use: ENIAC (for “Electronic Numerical Integrator and Computer”). “Programming” the machine involved technicians spending tedious days reconnecting cables and resetting switches by hand. It thus fell short of the modern computer, which stores its instructions in the form of coded numbers, or “software.”
Von Neumann aspired to create a machine that, as Dyson said “broke the distinction between numbers that mean things and numbers that do things” rel: Magic Action Words Turing Cathedral by George Dyson
Small sun: The possibility of such a “superbomb”—one that would, in effect, bring a small sun into existence without the gravity that keeps the sun from flying apart—had been foreseen as early as 1942.
Smarter, Happier, More Productive
1994 Gutenberg Elegies - computer and other electronic media were destroying our capacity for “deep reading.” Readers had become skimmers and scrollers.
Intellect decay Once new neural circuits become established in our brains, they demand to be fed, and they can hijack brain areas devoted to valuable mental skills. Thus, Carr writes, “the possibility of intellectual decay is inherent in the malleability of our brains.”
Many in neuroscience community scoff at the claims “the brain is not a blob of clay pounded into shape by experience.”
The digerati are not impressed by such avowals. “No one reads War and Peace,” responds Clay Shirky, a digital-media scholar at New York University. “The reading public has increasingly decided that Tolstoy’s sacred work isn’t actually worth the time it takes to read it.”
His point: *The only reason we used to read big long novels before the advent of the Internet was that we were living in an information-impoverished environment. Our “pleasure cycles” are now tied to the tech.
beyond a certain minimum IQ threshold—about one standard deviation above average, or an IQ of 115—there is no correlation at all between intelligence and creativity.
The Cosmos Reconsidered
String Theory Wars
The key insight is that the smallest constituents of the world are not particles, as had been supposed since ancient times, but “strings”—tiny strands of energy. By vibrating in different ways, these strings produce the essential phenomena of nature, the way violin strings produce musical notes.
All that remains to be done is to write down the actual equations.
Each of these critics of string theory delivers a bill of indictment that is a mixture of science, philosophy, aesthetics, and, surprisingly, sociology.
Nothing about it can be modified without destroying its logical structure. The physicist Steven Weinberg has compared it to Raphael’s Holy Family, in which every figure on the canvas is perfectly placed and there is nothing you would have wanted the artist to do differently.
Everything in the perfect place
I’ve had this thought with certain music tracks. Everything seems to be in the right place, to the extent I could not imagine it any other way. But also, I am repulsed by this thought.
String theory came into existence almost by accident. 1960s, young physicists thumbing through books, centuries old formula, the Euler beta function, that seemed to fit the experimental data about elementary particles. If tiny particles were thought of as wriggling strings (“tiny one dimensional rips in the smooth fabric of space”) it made sense.
Witten: Five distinct theories were mere facets of M-Theory. What M meant, “M stands for Magic, Mystery, or Membrane, according to taste.” Also later, Murky. Others offered “Matrix”, “Mother” and “Masturbation.”
In the past century, physicists who have followed their aesthetic sense in the absence of experimental data seem to have done quite well As Paul Dirac said, “Anyone who appreciates the fundamental harmony connecting the way Nature runs and general mathematical principles must feel that a theory with the beauty and elegance of Einstein’s theory has to be substantially correct.”
The idea that “beauty is truth, truth beauty” may be a beautiful one, but is there any reason to think it is true? Truth, after all, is a relationship between a theory and the world, whereas beauty is a relationship between a theory and the mind. Perhaps, some have conjectured, a kind of cultural Darwinism has drilled it into us to take aesthetic pleasure in theories that are more likely to be true. Or perhaps physicists are somehow inclined to choose problems that have beautiful solutions rather than messy ones. Or perhaps nature itself, at its most fundamental level, possesses an abstract beauty that a true theory is bound to mirror. What makes all these explanations suspect is that standards of theoretical beauty tend to be ephemeral, routinely getting overthrown in scientific revolutions. “Every property that has at some date been seen as aesthetically attractive in theories has at other times been judged as displeasing or aesthetically neutral,” James W. McAllister, a philosopher of science, has observed.
The current problem with Physics according to Smolin, is a problem of style: Initiators like Einstein, Bohr, Schrodinger and Heisenberg were deep thinkers. They confronted questions in a philosophical way. The new theories they created were essential correct. Development of these theories requires hard technical work, so for several generations normal science was dominated by “master craftspeople.” The problem with modern string theory, lots of promise with little fulfillment, is what you get when these craftsmen try to do the work of the original seers.
Einstein, Spooky Action and Reality of Space
What the principle of locality says, in essence, is that the world consists of separately existing physical objects and that these objects can directly affect one another only if they come into contact.
Einstein dismissed the possibility of voodoo-like, space-defying, nonlocal influences as “spooky action at a distance” (spukhafte Fernwirkung).
How Will the Universe End?
No matter where you are located, the rest of the universe would eventually be receding from you at the speed of light, slipping forever beyond the horizon of knowability. Meanwhile, the shrinking region of space still accessible to you would be filling up with a kind of insidious radiation that would eventually choke off information processing—and with it the very possibility of thought.
NOTE
eschatology from the green word “farthest”
Dyson’s “Time Without End”
In 1979, he wrote a paper called “Time Without End,” in which he used the laws of physics to show how humanity could flourish eternally in a slowly expanding universe, even as the stars died and the chill became absolute. The trick is to match your metabolism to the falling temperature, thinking your thoughts ever more slowly and hibernating for longer and longer periods while extraneous information is dumped into the void as waste heat. In this way, Dyson calculated, a complex society could go on perpetually with a finite energy reserve, one equivalent to a mere eight hours of sunlight
“The most plausible answer,” Dyson said, “is that conscious life will take the form of interstellar dust clouds.” He was alluding to the kinds of inorganic life-forms imagined by the late astronomer Sir Fred Hoyle in his 1957 science-fiction novel, The Black Cloud. “An ever-expanding network of charged dust particles, communicating by electromagnetic forces, has all the complexity necessary for thinking an infinite number of novel thoughts.”
Misc
It should be remembered that while Gödel was supremely logical, he was also supremely paranoid and not a little naive. There was something sweetly Pnin-like about him. He believed in ghosts; had a morbid dread of refrigerator gases; pronounced the pink flamingo that his hoydenish wife placed outside his window furchtbar herzig (awfully charming); and was convinced, based on nose measurements he had made on a newspaper photograph, that General MacArthur had been replaced by an impostor. His paranoia, though, was decidedly tragic. “Certain forces” were at work in the world “directly submerging the good,” he believed.